In communications networks, there may be a challenge to obtain good performance and capacity for a given communications protocol, its parameters and the physical environment in which the communications network is deployed.
For example, one parameter in providing good performance and capacity for a given communications protocol in a communications network is bandwidth. The bandwidth limits the information rate of a communication system and is a limited resource, hence it should be used efficiently. For this reason, faster-than-Nyquist (FTN) signaling has attracted interest as it enables a higher data rate (in comparison to schemes not using FTN signaling) without increasing the bandwidth, either by performing spectral compression or by transmitting pulses with a given time-domain shape at a rate that violates Nyquist's intersymbol interference (ISI) criterion. Since the pioneering work by Saltzberg (“Intersymbol interference error bounds with application to ideal bandlimited signaling,” IEEE Transactions on Information Theory, vol. 14, no. 4, pp. 563-568, 1968) and by Mazo (“Faster-than-Nyquist signaling,” Bell System Technical Journal, vol. 54, no. 8, pp. 1451-1462, 1975) researchers have been investigating the performance limits of FTN and methods for practical implementation.
FTN has traditionally required the use of the Viterbi algorithm for reliable decoding, an approach whose complexity grows exponentially with the number of interfering symbols and polynomially with the number of points in the signal constellation. As an example, decoding a M-PAM (where PAM is short for pulse-amplitude modulation) signal with N symbols and an effect of ISI lasting K symbols results in a computational complexity of O(N·MK). For large K and/or M this algorithm becomes impractical to be used.
Using the Viterbi algorithm for data decisions in the presence of ISI is thus computationally demanding if the modulation order is high (i.e., the value of M is large) and/or there is ISI interaction between many symbols (i.e., the value of K is large).
In general terms, the task of the receiver is to estimate the transmitted symbols based on the received symbols. Receivers for FTN signaling need to handle both ISI and colored noise (with a different covariance than the ISI). Optimal decoding is known to be a Non-deterministic Polynomial-time hard problem. Further, known mechanisms for decoding of FTN signaling operate on batches, which means that, in order not to lose accuracy, a full block needs to be received until the decoding can begin. Further still, known mechanisms for decoding of FTN signaling require large amounts of storage; to take ISI of length n into account (i.e., ISI affecting n transmitted symbols), O(n2) matrix elements need to be stored.
Hence, there is a need for an improved processing of a reception signal.